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1.9: Chapter 1 Review

Created by: CK-12

Define the following words:

  1. Domain
  2. Range
  3. Solution
  4. Evaluate
  5. Substitute
  6. Operation
  7. Variable
  8. Algebraic expression
  9. Equation
  10. Algebraic inequality
  11. Function
  12. Independent variable

Evaluate the following expressions.

  1. 3y (7 - (z - y)); use y = -7 and z = 2
  2. \frac{m + 3n - p}{4}; use m = 9, \ n = 7, and p = 2
  3. |p| - \left (\frac{n}{2} \right )^3; use n = 2 and p = 3
  4. |v-21|, \ v=-70

Choose an appropriate variable to describe the situation.

  1. The number of candies you can eat in a day
  2. The number of tomatoes a plant can grow
  3. The number of cats at a humane society
  4. The amount of snow on the ground
  5. The number of water skiers on a lake
  6. The number of geese migrating south
  7. The number of people at a trade show

The surface area of a sphere is found by the formula A = 4 \pi r^2. Determine the surface area for the following radii/diameters.

  1. radius=10 \ inches
  2. radius=2.4 \ cm
  3. diameter=19 \ meters
  4. radius=0.98 \ mm
  5. diameter=5.5 \ inches

Insert parentheses to make a true equation.

  1. 1 + 2 \cdot 3 + 4 = 15
  2. 5 \cdot 3 - 2 + 6 = 35
  3. 3 + 1 \cdot 7 - 2^2 \cdot 9 - 7 = 24
  4. 4 + 6 \cdot 2 \cdot 5 - 3 = 40
  5. 3^2 + 2 \cdot 7 - 4 = 33

Translate the following into an algebraic equation or inequality.

  1. Thirty-seven more than a number is 612.
  2. The product of u and –7 equals 343.
  3. The quotient of k and 18
  4. Eleven less than a number is 43.
  5. A number divided by –9 is –78.
  6. The difference between 8 and h is 25.
  7. The product of 8, –2, and r
  8. Four plus m is less than or equal to 19.
  9. Six is less than c.
  10. Forty-two less than y is greater than 57.

Write the pattern shown in the table with words and with an algebraic equation.

  1. &\text{Movies watched} && 0 && 1 && 2 && 3 && 4 && 5\\&\text{Total time} && 0 && 1.5 && 3 && 4.5 && 6 && 7.5
  2. A case of donuts is sold by the half-dozen. Suppose 168 people purchase cases of donuts. How many individual donuts have been sold?
  3. Write an inequality to represent the situation: Peter’s Lawn Mowing Service charges $10 per mowing job and $35 per landscaping job. Peter earns at least $8,600 each summer.

Check that the given number is a solution to the given equation or inequality.

  1. t=0.9, \ 54 \le 7(9t+5)
  2. f=2; \ f+2+5f = 14
  3. p=-6; \ 4p-5p \le 5
  4. Logan has a cell phone service that charges $18 dollars per month and $0.05 per text message. Represent Logan’s monthly cost as a function of the number of texts he sends per month.
  5. An online video club charges $14.99 per month. Represent the total cost of the video club as a function of the number of months that someone has been a member.
  6. What is the domain and range for the following graph?
  7. Henry invested $5,100 in a vending machine service. Each machine pays him $128. How many machines does Henry need to install to break even?
  8. Is the following relation a function?

Solve the following questions using the 4-step problem-solving plan.

  1. Together, the Raccoons and the Pelicans won 38 games. If the Raccoons won 13 games, how many games did the Pelicans win?
  2. Elmville has 250 fewer people than Maplewood. Elmville has 900 people. How many people live in Maplewood?
  3. The cell phone Bonus Plan gives you 4 times as many minutes as the Basic Plan. The Bonus Plan gives you a total of 1200 minutes. How many minutes does the Basic Plan give?
  4. Margarite exercised for 24 minutes each day for a week. How many total minutes did Margarite exercise?
  5. The downtown theater costs $1.50 less than the mall theater. Each ticket at the downtown theater costs $8. How much do tickets at the mall theater cost?
  6. Mega Tape has 75 more feet of tape than everyday tape. A roll of Mega Tape has 225 feet of tape. How many feet does everyday tape have?
  7. In bowling DeWayne got 3.5 times as many strikes as Junior. If DeWayne got 28 strikes, how many strikes did Junior get?

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